Movement 411 is a wheeled surveyor's carriage built around an isosceles triangle, a gravity pendulum and a paper drum driven from a carriage wheel. The pendulum pencil traces the ground profile as the carriage travels.
Self-recording Surveyor's Level Geometry
Explore ideal constant-slope geometry for the historical wheeled pendulum-and-chart survey recorder.
Equation Used
- Ground slope is constant over the selected travel.
- The rigid triangle base is parallel to the ground and wheel circumference equals that base.
- Wheels roll without slip and wheel-to-drum ratio is 1:1.
- Chart calibration, pencil linkage, backlash and pendulum dynamics are excluded.
The drum-revolution output explicitly assumes one drum revolution per wheel revolution.
Historical carriage recorder
The source states that the triangle has a horizontal base, each wheel circumference equals that base, the pendulum shifts from center on an incline, and gearing from one wheel rotates the ruled-paper drum.
This is not a float-pot hydrostatic level. The former float-arm calculator described a different instrument and has been removed.
What the calculator determines
Select constant ground slope α, triangle base b, perpendicular triangle height H and travel distance s. The ideal geometry reports wheel diameter b/π, pendulum intersection offset H tan α, wheel/drum revolutions s/b and elevation change s tan α.
Ideal constant-slope relations
The source condition Cwheel = b gives D = b/π. Taking uphill along the base as positive, a world-vertical pendulum intersects the base at the signed downhill offset x = −H tan α. With no slip and an assumed 1:1 wheel-to-drum rotation, n = s/b. Constant-slope elevation change is Δz = s tan α.
Selected-input arithmetic
For α = 5°, b = 600 mm, H = 400 mm and s = 10,000 mm, wheel diameter is about 191.0 mm, pendulum offset 35.0 mm, travel is 16.667 wheel turns and elevation change is about 874.9 mm.
Model boundary
The calculation is exact only for an ideal rigid carriage on one constant slope with no wheel slip and a stated 1:1 drum relation. The historical description does not specify gearing ratio, pencil linkage, chart scale, drum dimensions, wheelbase dynamics or calibration. Curved profiles, discrete sampling, backlash, pendulum oscillation and measurement error are excluded.
Questions
Why does wheel circumference equal triangle base?
That is an explicit proportion in movement 411.
Does the chart directly use millimetres?
Not from the source description alone; chart calibration and gearing remain unresolved.
Is this a modern survey instrument?
No. It is an educational model of the historical mechanical recorder.
References & Further Reading
- Wikipedia contributors. Levelling. Wikipedia
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